Gyrocompassing by intermittent GPS interferometry

ABSTRACT

The invention described here concerns the use of GPS (Global Positioning System) interferometry, or any similar satellite constellation, to estimate the attitude of a vehicle, and is particularly suited for LEO (Low Earth Orbit) satellites. The invention is based on a system of gyroscopic and interferometric sensors and a piece of software to process the data received by such sensors. The invention can be applied to any type of vehicle (terrestrial, naval, aircraft or spacecraft) to determine the attitude of the vehicle with respect to an inertial reference system.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a national stage of PCT/IT99/00315 filed Oct. 8,1999 and based upon Italian national application RM 98 A 000638 of Oct.12, 1998 under the International Convention.

TECHNICAL FIELD

The invention described here relates to the use of GPS (GlobalPositioning System) interferometry, or any similar satelliteconstellation, to estimate the attitude of a vehicle, and isparticularly suited for LEO (Low Earth Orbit) satellites. The inventioncan be applied to any type of vehicle (terrestrial, naval, aircraft orspacecraft) to determine the attitude of the vehicle with respect to aninertial reference system.

BACKGROUND ART

According to the present state of the art, in order to calculate theattitude of a vehicle, it is necessary to have two microwave sources inknown positions of space. The presence of the GPS constellation realizesthis condition and in fact various instruments are today available forsuch measurements (see references G and H).

Those instruments are designed to provide independent attitudemeasurements on three axes. The use of gyroscopic instrumentation isoptional, and it is not needed for attitude measurement, but only tofilter high frequency noise on measurement outputs. The basic schemedescribed in the literature (see references A and B) for satelliteattitude estimation consists of:

a constellation of N source satellites, each of which broadcasts anelectromagnetic signal which makes it possible to performinterferometric measurements; and

a receiver having four antennas (one of which for redundancy) pointed inthe same direction.

According to the scheme indicated above, the differential phasemeasurement is performed by two pairs of antennas with respect to allthe N satellites in the visibility field (a source satellite is meant tobe in the visibility field when the signal coming from the satellite hasa satisfactory signal-to-noise ratio). We have therefore a system of 2Nequations in the three attitude unknowns. This system is solved by thepseudo-inverse method (least square solution).

A necessary condition for the solution of attitude equations is thatthere should be at least two source satellites in the visibility fieldof the antenna network. The accuracy of estimate depends on thedifferential phase errors due to an unbalancing of the hardwaremeasurement device, or on phase errors caused by mutual interactionamong antennas (multipath errors), or on a misalignment of antennas.

The antennas commonly used for this purpose are antennas having a widefield of view (70-80 degrees of visibility cone), which are often notsuitable for interferometric measurements in terms of thermalsensitivity, phase measurement stability and coupling with satellitestructure. This results in limitations for attitude estimation accuracyfor those kind of methods. The following references summarize the stateof the art relative to the invention described below.

A. J. K. BROCK: GPS Tensor-GPS receiver for attitude and orbitdetermination, ION-GPS 95, Palm Springs, Sept. 1995.

B. J. K. BROCK, R. FULLER, S. HUR-DIAZ, J. RODDEN: “GPS Attitude andOrbit Determination for Space”, Palo Alto, Calif. 94303.

C. C. E. COHEN: Attitude Determination Using GPS, Ph.D. Dissertation,Dec. 1992, Stanford University.

D. S. J. FUJIKAWA, D. F. ZIMBELMAN: “Spacecraft Attitude Determinationby Kalman Filtering of Global Positioning System Signals”, Journal ofGuidance, Control and Dynamics, 1995.

E. R. FULLER, S. GOMEZ, L. MARRADI, J. RODDEN: “GPS AttitudeDetermination From Double Difference Differential Phase Measurements”,ION-GPS 96, Kansas City, Sept. 1996.

The invention is described now in its essential aspects. The gyro makesit possible to calculate attitude variations but not absolute attitudeitself. The basic principle of the invention rests on the fact thatinterferometric measurements can be correlated with each other, even ifmade in different moments or along different axes, due to thereconstruction that the gyro is able to do of the relative attitudevariations in the various measurement times.

For this purpose, it is necessary to compare gyro output signals withthose from an interferometer not at the attitude angle measurementlevel, but at the interferometric measurement level, performing a moreefficient dynamic filtering of measurements.

Dynamic filtering is performed by an observer structure in whichresiduals are directly computed as differences between interferometricmeasurements of phase and estimated values.

If the vehicle motion is not inertial, as is the case withEarth-pointing satellites, substantial advantages come from this:

attitude estimation requires only one source satellite in the field ofview even intermittently (more than one satellite improves estimationbut is not required; if the residual between interferometer and gyrowere made on attitude angles, then at least two satellites would berequired);

GPS interferometry can be used with a narrow antenna field of view(typically 20 or 30 degrees for semi-cone angle) around the Nadirdirection, avoiding collection of differential phase measurements in thelowest quality phase pattern zones (this makes it possible to have anaccuracy less dependent on the satellite configuration and multipathproblems);

The particular type of dynamic filtering makes possible an on-lineestimate of misalignments and constant phase errors (such acharacteristic improves the overall system accuracy; the estimatingfilter speed of convergence depends on the orbital velocity and thisfunction is particularly suited to LEO satellites, less suited toterrestrial vehicles).

The attitude measurement configuration described here consists of athree-axis gyroscopic sensor and an interferometric sensor having atleast three antennas (plus one for redundancy) far apart from eachother, a piece of processing software common to the two sensors andworking on the raw data provided by the sensors (differential phases andangular velocities). The piece of processing software only needs, as itsinput, the position occupied by the source satellites and user vehicleand provides, as its output, estimates of the attitude and of themisalignment between the antenna system and the gyro reference system.The use of the gyroscopic instrumentation is similar to the oneclassically known as “gyrocompassing” and described in reference 1.

The described measurement configuration is capable of working for anykind of vehicle, however performance depends on the user vehicletrajectory and on the visibility of source satellites during thetrajectory.

In the case of inertial pointing satellites, there is no chance ofobserving misalignments and receiver line offsets; then an operativestep of calibration of Earth pointing should be taken. For illustrativebut not limiting purposes, the description is now limited to the case ofEarth pointing LEO satellites. The invention, however, can be applied toany vehicle.

BRIEF DESCRIPTION OF THE DRAWING

In the drawing:

FIG. 1 is a diagram of a satellite system;

FIG. 2 is a more detailed view of the satellite; and

FIG. 3 is a block diagram.

SPECIFIC DESCRIPTION

FIG. 1 shows the user vehicle 11 (in this case, a satellite) with itsreference system x₀, y₀, z₀, the visibility cone 14 with itssemi-aperture angle θ, and the source satellite 10.

FIG. 2 provides particulars of satellite 11. FIG. 2 shows satellite 11with four receiving antennas 12 mounted in Zenith direction on amounting cone 13 placed on the panel opposite to the Earth direction ofsatellite 11.

FIG. 3 shows a block scheme of he estimator, as better described below.

When a satellite belonging to a constellation of source satellites, likeGPS, comes into the visibility cone (i.e. 20° off-Nadir), aninterferometric measurement is made possible (see FIG. 1).

The choice of receiving antennas depends on the system requirements. Anantenna having a broad beam width, as is the case with the “micro-strippatches”, has usually strong and hardly modellable multipath effects.The best choice for a high performance system is a medium-beam antennahaving a low temperature-dependent error of tracking. The multipath dueto such mobile surfaces of the satellite as solar panels should be keptoutside the visibility cone.

For this purpose, mounting the antennas on a high cone (see FIG. 2) onthe satellite makes the system able to reach superior performance.

As an example, with reference to FIG. 2, a satellite 11 having fourantennas 12, each with a 60 degree beam width, mounted on a 30 cm highcone 13 is capable to restrain multipath errors in a semi-cone field of30° of about ±+2°, which can change with temperature by ±+1 phasedegrees. Additional constant errors that can be calibrated (includingreceiver bias) are about 5 phase degrees in magnitude. (Note: 1 degreein phase error corresponds to 0.03 degrees in attitude angle error, fora distance of 1 m between the antennas).

The estimator structure is shown in FIG. 3. The on board softwarecomponents are identified by using white boxes, whereas gray boxes areused to represent physical sensors.

The internal algorithms for each component are strictly related to thefunction performed by that component, for any specific implementation ofthe present invention. For this reason, the mathematical structure ofsuch algorithms is not described here. Referring to FIG. 3, the symbolsshown are:

t: time (On Board Reference Time);

v: visibility of the microwave source(s);

s: direction of the source in orbital reference frame;

Φ: attitude relative to orbital reference frame;

ω: inertial angular velocity;

{circumflex over (ω)}: estimated inertial angular velocity;

ω₀ : orbital angular velocity;

What is claimed is:
 1. System based on GPS (Global Positioning System)interferometry or on any similar satellite constellation to measure theattitude of a vehicle (11), said system comprising: a three-axisgyroscopic sensor (9); an interferometric sensor (8) with multipleantennas (12), having at least three antennas, which measures thedifferential phase of the electromagnetic waves generated by sourcesatellites (10), a piece of software for processing the data coming fromsaid interferometric sensor (8) and from said gyroscopic sensor (9);said piece of software comprising in turn orbital dynamics (1) whichrepresents the equations providing the angular velocity of the orbitreference frame at a given time, interferometer model (2) which providesthe interferometric measurements expected and their derivatives on thebasis of the positions of said source satellites (10), of the calibratedmisalignments and of the esteemed attitude, pre-filter (3) whichperforms the functions of pre-filtering on the interferometricmeasurements and of pseudo-derivator, pre-filter (5) which performs thepre-filtering of the signals coming from said gyroscopic sensor,estimator (4) which, starting from the residuals between saidinterferometric measurements and their derivatives and between saidinterferometric measurements expected and their derivatives, producesfeedback of attitude angles on the observer, kinematics (6) whichcalculates the attitude angles with respect to orbit reference framestarting from the relative inertial angular velocity of said vehicle(11) with respect to orbit reference frame, integrator (7) whichintegrates the differential equations of said estimator (4); said pieceof software being constructed and arranged to perform the followingfunctions: decoding of the positions of said source satellites (10) and,through the processing of the data coming from said source satellites(10), determination of the position of said vehicle (11); calculation ofthe three-axis attitude of said vehicle (11); calculation of theconstant measurement error of said interferometer (8) with respect tothe natural reference frame of said gyroscope (9); said estimator (4)uses the difference between the measurements from said interferometer(8) and the prediction of said measurements, as residuals whereby themeasurements of the attitude of said vehicle is performed even if onlyone of said sources satellites (10) is in the field of view of saidvehicle (11); the attitude measurements of said vehicle (11) isperformed even in conditions of temporary invisibility of said sourcesatellites (10); and said estimator (4) performs on-line the calibrationof static errors of measurements of differential phase.
 2. The systemclaimed in claim 1 wherein said source satellites (10) may be one, or aconstellation of satellites, or more constellations of satellites. 3.The system claim in claim 1 wherein said system can work for any type ofsaid vehicle (11), and when said vehicle (11) is a satellite.
 4. Systembased on GPS (Global Positioning System) interferometry or on anysimilar satellite constellation to measure the attitude of a vehicle(11), said system comprising: a three-axis gyroscopic sensor (9); aninterferometric sensor (8) with multiple antennas (12), having at leastthree antennas, which measures the differential phase of theelectromagnetic waves generated by source satellites (10), a piece ofsoftware for processing the data coming from said interferometric sensor(8) and from said gyroscopic sensor (9); said piece of softwarecomprising in turn orbital dynamics (1) which represents the equationsproviding the angular velocity of the orbit reference frame at a giventime, interferometer model (2) which provides the interferometricmeasurements expected and their derivatives on the basis of thepositions of said source satellites (10), of the calibratedmisalignments and of the esteemed attitude, pre-filter (3) whichperforms the functions of pre-filtering on the interferometricmeasurements and of pseudo-derivator, pre-filter (5) which performs thepre-filtering of the signals coming from said gyroscopic sensor,estimator (4) which, starting from the residuals between saidinterferometric measurements and their derivatives and between saidinterferometric measurements expected and their derivatives, producesfeedback of attitude angles on the observer, kinematics (6) whichcalculates the attitude angles with respect to orbit reference framestarting from the relative inertial angular velocity of said vehicle(11) with respect to orbit reference frame, integrator (7) whichintegrates the differential equations of said estimator (4); said pieceof software being constructed and arranged to perform the followingfunctions: decoding of the positions of said source satellites (10) and,through the processing of the data coming from said source satellites(10), determination of the position of said vehicle (11); calculation ofthe three-axis attitude of said vehicle (11); calculation of theconstant measurement error of said interferometer (8) with respect tothe natural reference frame of said gyroscope (9); said estimator (4)uses the difference between the measurements from said interferometer(8) and the prediction of said measurements, as residuals whereby themeasurements of the attitude of said vehicle is performed even if onlyone of said sources satellites (10) is in the field of view of saidvehicle (11); the attitude measurements of said vehicle (11) isperformed even in conditions of temporary invisibility of said sourcesatellites (10); and said estimator (4) performs on-line the calibrationof static errors of measurements of differential phase, wherein saidsystem can work for any type of said antennas (12) including antennas(12) provided with a thermal control system, or stable with temperatureto 3 degrees of phase in the operating interval of temperatures, saidantennas (12) having such a mounting system on said vehicle (11) or suchan electromagnetic configuration as to contain the phase error due tomultipath below 3 degrees in a visibility cone of 30 degrees from theaxis of an antenna (12).